When ice melts in a full glass of water, will the water overflow

• bobsmith76
In summary: There is no definitive answer, as the amount of buoyancy will vary depending on the specific material and construction of the ice cube.
bobsmith76
If you have an ice cube in a full glass of water when the ice cube melts will the water flow over, be the same, or decrease? My book says the answer is stay the same, but I can't figure out why. Ice was less dense than water which is why is floats. Using this equation:

B = ρVg which when solved for V becomes

B/(ρg) = V

I would think the buoyancy would stay the same as the ice cube melts so the density ρ increases as the ice melts, so if you increase the denominator, the whole number decreases. So the water should decrease, not stay the same, unless the increase in density is compensated for by an increase in Buoyancy.

I shouldn't just hand this to you, I should walk you through it, but you're made some effort - and the diagram is right there...

An also interesting question would be why the melting of icebergs increase the level of oceans (I think it does, but I could be wrong).

Ok, I'm using this equation now

ρwaterAh = ρcubeVcube

As the volume decreases so too does the area and the height.

bobsmith76 said:
If you have an ice cube in a full glass of water when the ice cube melts will the water flow over, be the same, or decrease?

One somewhat novel exception is that that if you had a higher density form of ice, such as ice III (or higher stage of ice), it would be resting on the bottom of the glass instead of floating. In this case, as it melts, the density would decrease and the water level would rise.

fluidistic said:
An also interesting question would be why the melting of icebergs increase the level of oceans.
It's the melting of glaciers which are currently supported by land masses, not the oceans. As they melt, the water eventually runs off into the oceans.

Ok thanks rcgldr!

If the ice cube was chained to the base of the glass, then as it melts, it turns into denser water, so the water level will lower.

If the ice cube is buoyant, then the amount of water it displaces is equal to its own WEIGHT (not mass as someone else wrote); as it melts, the water level remains the same. The ice cube is less dense than water, so it will be "sticking up" above the water, and as it melts, it turns into denser water, occupying the same volume as the submerged portion of the ice cube.

If the ice cube had helium bubbles in it, then the helium would add even greater buoyancy, as it has negative weight against the atmosphere, and as the helium leaked out, the ice cube would WEIGH more (even though, without the helium bubbles, it has less mass), and so the water level will rise.

It is important to distinguish weight and mass. There's only a notion of "displacing" water because there's a force applied on the water to _prevent_ it from natural displacement (brownian motion). In this case, gravity and the contours of the glass. The water has a downward force keeping it from naturally flying out of the glass (gravity) - a weigh scale can measure this force. A buoyant object also applies a downward force - again measurable by a weigh scale. The water moves /upward/ in the presence of the buoyant object trying to go /downward/ because of the contours of the glass. If the glass were a pipe, you've just re-invented a pipe-cleaner and helped the liquid move further down the pipe. Because the glass has a strong bottom, the /bottom/ of the glass applies an upward force against the water. The water level then rises as the buoyant object submerges. If the only forces involved are gravity, then you'll get the same answer whether you use mass or weight, but if you introduce any other forces, the upward force on helium, or the downward force of a magnetic field tugging a buoyant object down, you'll get the incorrect answer using mass. For example, if you have an iron warship and a magnetic field pushing it downward, it will displace more water than an iron warship of equal mass without that additional downward force.

Last edited:

Would it be mischievous to point out that the melting of the ice cube will change the temperature of the water, and hence its volume?

Of course this effect will be temporary; eventually the whole thing returns to ambient temperature.

Last edited:
Think of a boat filled with ice that's floating in a lake. The ice in the boat melts, but the mass doesn't change, and the waterline stays the same.

There are some modifications to that question:

What happens to the water level during melting if the ice has...

a) ... a cavity with air inside?

b) ... a cavity with molten water inside?

c) ... a piece of lead inside?

Nugatory said:
Would it be mischievous to point out that the melting of the ice cube will change the temperature of the water, and hence its volume?

Of course this effect will be temporary; eventually the whole thing returns to ambient temperature.

No, that is already covered by the temperature causing the water to be ice. Think of the water and ice as a closed system and consider the average temperature of this system.

When Ice Melts in a Full Glass of Water, Will the Water Overflow?

Many people wonder what happens when ice melts in a full glass of water. Let's explore the science behind it:

Q1: Does the Water Overflow When Ice Melts in a Full Glass?

No, the water does not overflow when ice melts in a full glass of water. In most cases, the level of the water remains the same. This is because the ice that melts in the glass was originally part of the water, so when it melts, it simply returns to its liquid state.

Q2: Why Doesn't the Water Overflow?

The principle at play here is Archimedes' principle, which states that an object submerged in a fluid (in this case, water) displaces an amount of fluid equal to its own volume. Since the ice was already in the glass, it had displaced its volume of water before melting. When it melts, the water it turns into is the same volume, so there is no net change in the water level.

Q3: What Happens When Ice Floats in Water?

Ice floats in water because it is less dense than liquid water. The unique property of water is that it reaches its maximum density at approximately 4 degrees Celsius (39.2 degrees Fahrenheit). Below this temperature, water becomes less dense, which is why ice floats. This property is essential for aquatic life in cold regions because it allows a layer of ice to form on the surface, insulating the water below and preventing it from freezing solid.

Q4: Is There Any Situation Where Water Might Overflow When Ice Melts?

Generally, ice melting in a full glass of water will not cause overflow. However, if the glass is already filled to the brim before the ice is added, there may be a slight overflow as the ice displaces some of the water. In such cases, it's advisable to leave some space at the top of the glass to accommodate the ice as it melts.

Q5: Does Temperature Affect the Outcome?

Temperature can influence the outcome to some extent. Warmer water may cause ice to melt more quickly, but the basic principle of displacement remains the same. The water level will adjust to accommodate the melted ice without overflowing.

Q6: Can You Explain Why Ice Expands When It Freezes?

Ice expands when it freezes due to the formation of a crystalline structure. In the process of freezing, water molecules arrange themselves in a hexagonal pattern, which creates open spaces between the molecules and results in an increase in volume. This expansion is why ice is less dense than liquid water and floats on its surface.

Replies
3
Views
3K
Replies
11
Views
1K
Replies
6
Views
2K
Replies
6
Views
1K
Replies
3
Views
1K
Replies
52
Views
7K
Replies
1
Views
3K
Replies
18
Views
53K
Replies
2
Views
2K
Replies
11
Views
1K